Constructing approximate inverse systems of metric spaces (Q5954668)

The author assigns to any cofinite approximate inverse system of metric spaces and uniformly continuous maps another such system with connecting maps belonging to a given system of maps. The result is then used to obtain new proofs and generalizations of several known results on inverse systems (like \textit{M. Brown}'s approximation theorem [Proc. Am. Math. Soc. 11, 478-483 (1960; Zbl 0113.37705)] and \textit{M. C. McCord}'s embedding theorem for approximate system [Can. J. Math. 19, 321-332 (1967; Zbl 0147.23001)]). Another application deals with \(\Pi\)-approximable spaces, where \(\Pi\) is a class of metric spaces (like complete metric spaces or compact polyhedra).